Some currently available attitude estimate systems or inertial navigation systems contain inertial sensors that include both high and low performance gyroscopes and high and low performance accelerometers in which the low performance gyroscopes and accelerometer sense axes are co-aligned parallel to the force of gravity, when in operation. In some cases, the low performance accelerometer is a micro-electro-mechanical system (MEMS) accelerometer. The heading estimate of such a device degrades when the low performance accelerometer is tilted so that the low performance sense axis is no longer optimally aligned parallel to the force of gravity. When this occurs, the sense axis of the low performance accelerometer begins to contribute to the computation of heading by the navigation algorithms and Kalman filter and the estimate of heading is degraded. Likewise, when the sense axis of the low performance gyroscopes are tilted to be non-parallel to the force of gravity or non-parallel to true north, the low performance gyroscopes begin to contribute to the computation of heading by the navigation algorithms and Kalman filter and the estimate of heading is degraded.
In some cases, the performance of the navigation algorithms and the Kalman filter is severely degraded when such a device is highly tilted or rotated from north. The performance degradation in heading is especially large when low performance MEMS accelerometers and gyroscopes are used in some axes.